Let $U, V$ be random numbers chosen independently from the interval $[0, 1]$ with uniform distribution. Find the cumulative distribution and density of each of the variable $Y = |U − V|$.
Attempt: I used $P (Y \le y)$, I took the positive side of the absolute value and got $P (U-V \le y)$. Later I thought about isolating $u$ to get $P (U \le y+V)$. Thus, I figured the cdf would be $F (y)=y+V$ after using a theorem.
Later, I tried to stretch the graph out in my head with the intervals from $[0,1]$. Then, I thought about the cdf and I thought it would be about $1-y$ because no matter what value you get, the function will be less than $1$ from the cdf, but it was still wrong. How should I find the correct cdf?